I was actually offline.
If you just set your status to 'Appear Offline' you are still online but only appear to be offline to your friends.
You can try changing only your status, but my guess is that this will not suffice.

Not sure why but it does (you can read more about it on forum of playstationtrophies - this is where I found the information).
The game does keep some kind of online leaderboard which allows you to compare your game completion percentage with friends.
This is I guess somehow tied to the condition which determines if you will get a trophy or not.

Information in the trophy guide and this thread is not correct.
It is still possible to get 'Über hero' trophy by playing only the last chapter on Über difficulty even if you have a pre-patched digital version of the game.
The trick is that you need to play the last chapter while your PS4 is offline.
This is how I got the trophy:
finished first 15 chapters on normal
then went offline and did last chapter on Über using chapter select
Did this with NA digital version of the game which comes pre-patched to 1.01.